Учебники / Middle Ear Mechanics in Research and Otology Huber 2006
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kHz). Compared with the experimental data in Fig. 2, the model-predicted umbodisplacementincreasedmoreafterC7orC1removalatf≤1kHz.Itis also noticed that the ligament removal did not a ect the umbo movement at high frequencies (f≥2 kHz) shown in the experiments (Fig. 2) and FE model(Fig.4).However,theumbodisplacementfromthemodeldecreased faster than that measured from the bones at frequencies 2 to 8 kHz.
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Fig. 4 FE model-derived umbo displacement curves under the normal and ligament removal sequence: C5C3C7C1. (A) Magnitude; (B) phase angle.
Fig. 5 shows the FE model-derived displacement curves of the stapes footplate under destruction of each ligament following the bone experimental sequence. The model results indicate that the removal of middle ear ligamentsonlya ectedthefootplatedisplacementatf<1kHzandtherewasno obvious di erence observed between ligaments. Similar to the umbo, the footplatedisplacementfromthemodeldecreasedfasterthanthatmeasured in bones at frequencies 1 to 8 kHz.
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Fig. 5 FE model-derived stapes footplate displacement curves under the normal and ligament removal sequence: C5C3C7C1. (A) Magnitude; (B) phase angle.
4. Discussion
Both experimental and FE modeling results show that destruction of middle ear ligaments/tendons a ects the TM and stapes footplate vibrations at low frequencies (f≤1 kHz). The tensor tympani tendon and superior mallear ligament may play a more important role for acoustic-mechanical transmission compared with other ligaments. The e ects of ligaments on transfer function of the middle ear are frequency sensitive and vary with individual ligaments.
To fully understand the function of middle ear ligaments on sound transmission, we must know mechanical properties of those tissues and theircombinedsystemfunctiononossicularchain.Ourrecentmechanical tests of middle ear ligaments and tendons have shown that the ear tissues are viscoelastic materials and the Young’s modulus changes with stress level. In this study, we employed the preliminary data obtained from uniaxial tensile tests on tendons C5 and C7, and ligament C4 into our model (The details of material tests are not shown here and two papers are currently under review). However, the ligament mechanical property data have improved the accuracy of the model for predicting the ligament function on umbo and stapes movements as compared with our previous model predicted results reported in 2004 ARO meeting.
In conclusion, it is expected that the e ect of middle ear suspensory ligaments on middle ear function is extended into several di erent cutting sequences in temporal bones. A more realistic model reflects middle ear ligaments and other soft tissue mechanical properties will be developed. The final conclusion on middle ear ligament function will be revealed in our future studies.
220Acknowledgments
TheauthorsthankKennethJ.Dormer,Ph.D.,forthetemporalboneexperiments. This work was supported by NIDCD and NSF grants.
References
1.Hüttenbrink K. B., The functional significance of the suspending ligaments of the ear ossicle chain. Laryngorhinootologie 68 (1989) pp. 146–151
2.Gan R. Z., Feng B. and Sun Q., Three-dimensional finite element modeling of human ear for sound transmission. Ann Biomed Eng 32 (2004) pp. 847–859
3.Nandapalan V., Pollak A., Langner A., and Fisch U., The anterior and superior malleal ligaments in otosclerosis. Otol Neurotol 23 (2002) pp. 854–861
4.Nakajima H. H., Ravicz M. E., Rosowski J. J., Peake W. T., and Merchant S. N., Experimental and clinical studies of malleus fixation. Laryngorhinootologie 115 (2005) pp. 147–154
5.Abdelhamid M. M., Paparella M. M., Schachern P. A., and Yoon T. H., Histopathology of the tensor tympani muscle in otitis media. Eur Arch Otorhinolaryngol, 248 (1990) pp. 71–78
6.Gan R. Z., Wood M. W. and Dormer K. J., Human middle ear transfer function measured by double laser interferometry system. Otol Neurotol 25 (2004) pp. 423– 435
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EVALUATION OF LASER VIBROMETRY AS DIAGNOSTIC UTILITY
BY MEANS OF A SIMULATION MODEL OF THE MIDDLE EAR
Matthias Bornitz1, Nikoloz Lasurashvili1, Hans-Jürgen Hardtke2, Thomas Zahnert1
Technische Universität Dresden
1 Dept. of Medicine, Clinic of Otorhinolaryngology, Fetscherstr. 74,
01307 Dresden, Germany
2 Dept. of Solid State Mechanics, 01062 Dresden, Germany Email: matthias.bornitz@tu-dresden.de
In this study we used a Finite Element model of the middle ear to evaluate LDV (Laser- Doppler-Vibrometer) measurements of sound induced umbo vibrations. Simulations were performed for the intact ossicular chain, otosclerosis, incus luxation and malleus head fixation. Simulation results are comparable to results from clinical investigations. Incus luxation and malleus head fixation can be clearly distinguished. Results for otosclerosis range from almost unchanged to moderate changes in umbo vibrations, depending on particular middle ear morphology.
1. Introduction
222Measurementsofsoundinducedumbovibrations(bymeansofLaserDoppler Vibrometry) have already been used in clinical studies to investigate their potential as a diagnostic utility [1–3]. The method is aimed to distinguish the di erent pathologies of conductive hearing loss and to evaluate the quality of reconstructive middle ear surgery. The clinical studies comprise patients with conductive hearing loss due to otosclerosis, incus luxation and bony malleus fixation [2]. In [3] the method was also used to evaluate post-stapedectomy results.
These measurements on patients are subject to some limitations. The measurements can only be done at one state per subject (ear), i.e. normal ear or pathologically changed ear. There is a great variance in the measurements due to individual variations. Measurements on normal ears from
di erent individuals di er in magnitude by up to 20 dB across the whole investigated frequency range. The same holds for measurements of pathologicalears.Herewealsohaveanadditionalproblemintermsoftheclassification of the pathological change. Di erent characteristics of one disease are normally assigned to one group. We also may have mixed pathologies where only the major one is detected.
Thus for measurements on subjects the question arises what pathologies can be reliably distinguished. And: can we observe a correlation between conductive hearing loss (from audiometric investigation) and changes in umbo vibration?
The main advantage of simulation models is that the intact ossicular chain and di erent pathologies can be studied at the same ear without the influence of inter-individual variations. Furthermore all parameters of the model can be modified separately, thus allowing to simulate a great variety of distinct changes of the ossicular chain. The main problem is that the model is validated against a normal ear and represents an average ear. The modifications in the model to simulate the pathological changes are sometimes very large and the validity of the model can not be assured. There may be also limitations for an adequate simulation of specific pathological changes since every model is based on simplifications. Thus simulation results and measurements should always be critically evaluated against each other.
The purpose of this work is to simulate di erent pathologies and their influenceonthetransferfunctionattheumboinordertoassisttheclinical investigations.
2. Method
We used a Finite Element Model of the middle ear for the investigations [4,5]. It has been developed for investigations on middle ear reconstruc- 223 tions with focus on the acoustic transfer characteristics and the frequen-
cy range of speech. Accordingly the model is limited to the linear region (sound pressure up to 110 dB) and to frequencies up to 6 kHz.
The model consists of the ear canal (acoustic fluid), the eardrum (orthotrop-elastic shell with constant damping ratio), the ossicles (rigid bodies with mass and inertia properties), ligaments (elastic bars), joints (elastic bodies with constant damping ratio) and a spring-mass-damper modelofthecochlea(valuestakenfrom[6]).Themodelandthecalculated quantities are presented in figure 1.
Calculations were performed according to the clinical measurements to get comparable results, i.e. a harmonic analysis in the frequency range
from 200 to 5000 Hz was done. A sound pressure was applied at the ear canal entrance and the reference pressure at the eardrum and the displacement of the umbo and the footplate were calculated. From that the frequency transfer function (FRF) between umbo displacement and sound pressure in front of the tympanic membrane was built (subsequently named umbo FRF). In order to consider realistic measurement conditions the umbo displacement was calculated as the mean displacement of all points within a 0.2 mm radius around the umbo. This accounts for variations in targeting the laser point to the umbo.
The calculated transfer function between stapes footplate displacement and sound pressure serves as indicator for the sound energy transfer to the inner ear. A reduction of the magnitude of this transfer function compared to the normal ear is thus comparable to a conductive hearing loss.
Fig. 1 Finite Element model of the middle ear. The ossicles were treated as rigid bodies and were simplified to bar structures. The calculated component of the umbo displacement is indicated by the arrow.
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Calculations were done for the intact middle ear and for the following pathological changes: malleus head fixation (sti ening of the superior malleal lig. up to osseous fixation), chain interruption, sti ening of the annular ligament (otosclerosis), sti ening of the IMJ (Incudo-Malleal-Joint) and the ISJ (Incudo-Stapedial-Joint). The model parameters were also slightly varied to account for the inter-individual variations.
The calculated umbo FRF of the normal middle ear model lies within thenormalrangeofmeasuredtransferfunctions[7](seefig.2).Smallvariations of the Young's modulus of the joints (IMJ and ISJ varying between 0.4 and 40 MPa) make a di erence of at most 10 dB in the FRF, which is also well within the range of individual variations.
3. Results
3.1 Ossicular chain interruption
Ossicular chain interruption leads to a shift of the first resonance peak to lower frequencies and to an increase in magnitude (fig. 2). This change can already be observed when the Young's modulus of the joint is reduced by a factorof100tosimulateahypermobilejoint.(TheYoung'smodulusof0.04 MPa then corresponds to that of very weak connective tissue.)
3.2 Ossicular joint fixation
IMJorISJfixationaswellasthefixationofbothjointsdonotmakeremarkable di erences in the umbo FRF. A maximum reduction of the magnitude of up to 10 dB in the lower frequency range can be observed when the IMJ is fixed. The umbo FRF is for all these cases within the range of normal ears [7] (fig. 2).
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Fig.2 Umbo FRF for intact ossicular chain and simulation of ISJ luxation, IMJ and ISJ fixation. The dashed lines indicate the 90% percentile of FRFs from measurements of normal ears [7], i.e. the normal range.
3.3 Otosclerosis, fixation of the annular ligament
Sti ening of the annular ligament leads to a reduced magnitude in the low frequency range and a shift of the resonance peak towards higher frequencies in the umbo FRF (fig. 3). The amount of these changes is strongly dependent on other parameters of the ossicular chain. When using the model with the initial set of parameters, the change in the umbo FRF was insig-
nificant (2nd line in fig. 3), even though the Young’s modulus of the annular ligament was increased by a factor of 1000, which is nearly osseous fixation.
Following that, some of the initial parameters of the model have been variedaccordingtonormalvariationsingeometryandmaterialproperties in normal ears. (For instance the ossicular joints, where sti ness parameters varying by at least a factor of 10 can be found across the literature.) When the ISJ sti ness was increased by a factor of 10 there was about no change in the umbo FRF. Combining this still normal ear with otosclerosis leads to remarkable changes in the umbo FRF (last two lines in fig. 3), whereas variations in the otosclerosis value do not equally show up in the umbo FRF (cp. last two lines in fig. 3).
The changes in the footplate transfer function were as expected. Reduction in magnitude is to the same degree as the increase of Young’s modulus of the annular ligament (fig. 4). Changes in the ISJ hardly influence the footplate FRF.
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Fig. 3 Umbo FRF for simulation of otosclerosis (increasing sti ness of the annular ligament).
Fig. 4 Footplate FRF for simulation of otosclerosis (increasing sti ness of the annular ligament).
3.4 Malleus head fixation
Fixation of the malleus head was simulated by stepwise increasing the sti - ness of the superior malleal ligament up to an osseous fixation. In case of osseous fixation the malleus is immobilized and there is a tremendous decrease in the magnitude of the umbo FRF. But this can only be observed if theFRFiscalculatedexactlyfortheumbonode(lastlineinfig.5).Ifamean displacement around the umbo is used the observed change in the umbo FRFismuchless(3rdlineinfig.5)butitisstillreliabletodistinguishfroma normalossicularchain.Inthecaseofpre-stagesofanosseousfixation(2nd line in fig. 5) the umbo FRF then is within the range of normal ears.
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